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I'm trying to place the align environment next to my enumerate item (here, the sigma sign should be next to "Induktionsschluss" and not displaced a bit downward). How to get it next to it?

\begin{enumerate}
\item Induktionsanfang $n = 0$: $\displaystyle\sum_{k=0}^0 q^k = q^0 = 1 = \frac{1 - q^1}{1 - q}$
\item Induktionsannahme: $\displaystyle \exists n \in \mathbb{N}_0: \sum_{k=0}^n q^k = \frac{1 - q^{n+1}}{1-q}$
\item Induktionsschluss:
\begin{align*}
\sum_{k=0}^{n+1} q^k &= \sum_{k=0}^n q^k + q^{n+1}
\\ &= \frac{1 - q^{n+1}}{1-q} + q^{n+1}
\\ &= \frac{1 - q^{n+1}}{1-q} + \frac{q^{n+1}(1-q)}{1-q}
\\ &= \frac{1 - q^{n+1} (1 - (1 - q))}{1-q}
\\ &= \frac{1 - q^{n+1} (1 - 1 + q)}{1-q}
\\ &= \frac{1 - q^{n+1}q}{1-q}
\\ &= \frac{1 - q^{n+2}}{1-q}
\end{align*}
\end{enumerate}

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Use the aligned environment with vertical placement option [t]:

\documentclass[11pt]{article}
\usepackage{geometry}
\usepackage[inline, shortlabels]{enumitem}
\usepackage{amsmath, amssymb}

\begin{document}

\begin{enumerate}
\item Induktionsanfang $n = 0$: $\displaystyle\sum_{k=0}^0 q^k = q^0 = 1 = \frac{1 - q^1}{1 - q}$
\item Induktionsannahme: $\displaystyle \exists n \in \mathbb{N}_0: \sum_{k=0}^n q^k = \frac{1 - q^{n+1}}{1-q}$
\item Induktionsschluss:
$ \displaystyle\begin{aligned}[t]
\sum_{k=0}^{n+1} q^k &= \sum_{k=0}^n q^k + q^{n+1}
\\ &= \frac{1 - q^{n+1}}{1-q} + q^{n+1}
\\ &= \frac{1 - q^{n+1}}{1-q} + \frac{q^{n+1}(1-q)}{1-q}
\\ &= \frac{1 - q^{n+1} (1 - (1 - q))}{1-q}
\\ &= \frac{1 - q^{n+1} (1 - 1 + q)}{1-q}
\\ &= \frac{1 - q^{n+1}q}{1-q}
\\ &= \frac{1 - q^{n+2}}{1-q}
\end{aligned} $
\end{enumerate}

\end{document} 

enter image description here

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